SOL 



SOL 



folid angle ; ^ = -i- circumference, or 1 80° ; and A the 

 plane angle made by two adjacent faces; then we have 



cof. ■ 



fm, 



|A 



Cn. 



This theorem gives for the plane angle formed by every 

 two contiguous faces of the tetraedron, 70° 31' 42"; of 

 the hexaedron, 90° ; of the oftaedron, 109° 28' 18" ; of the 

 dodecaedron, ii6'33' 54"; of the icofaedron, 138° 11' 23". 

 But in thefe polyedras, the number of faces meeting about 

 each folid angle are 3, 3, 4, 3, 5, refpeftively. Confe- 

 queiitly the fohd angles will be determined by the fubjoined 

 proportions. 



-3( 7o°3i'4z")-i8o' 



3(90°) -180^ 



360°: 1000:: <! 4(i09°28'i8")-i8o= 



3(ii6°33'54") 

 .5(i38°n'23") 



: 87.736 tetrae. 



; 250 hexae. 

 216.351 oftae. 

 180° : 47 1.395 dodecac. 

 180°: 419.301 icofae. 



3. Solid angles at the vertices of cones, will be deter- 

 mined by means of the fpheric fegments cut off at the 

 bafes of thofe cones ; that is, if right cones, inftead of 

 having plane bafes, had bafes formed of the fegments of 

 equal fpheres, whofe centres were the vertices of cones, the 

 furface of thofe fegments would be the meafures of the 

 folid angles at the refpeftive vertices. Now the furface of 

 fpheric fegments, is to the furface of the hemifphere, as 

 the altitudes to the radius of the fphere ; and, therefore, 

 the folid angle at the vertices of right cones, will be to 

 the maximum fohd angle, as the excefs of the flant fide 

 above the axis of the cone, to the flant fide of the cone. 

 Thus, if we wifh to afcertain the folid angles at the ver- 

 tices of the equilateral and right-angled cones ; the axis of 

 the former is ^ y 3, and of the latter 4 ^ 2, the flant fide 

 of each being unity. H«nce, 



3 :: 1000 : 133-97 angleatvertexequilateralcone. 



■ Y A' 



I : 



1:1 — 4^/2:: 1000 : 292.98 - - right-angled.. 



4. From what has been faid, the mode of determining 

 the folid angles at the vertices of pyramids will be fuffi- 

 ciently obvious. If the pyramids be regular ones, and N 

 reprefent the number of faces meeting about the vertical 

 angle in one, and A the angle of inclination of each two 

 of its plane faces ; alfo n the number of planes meeting 

 about the vertex of another, and a the angle of inclination 

 of each two of its faces ; then will the vertical angle of 

 the former, be to the vertical angle of the latter, as 



NA — (N - 2) 180°, to na — (n — 2) 180°. 



If a cube be cut by diagonal planes into fix equal pyra- 

 mids, with fquare bafes, their vertices all meeting in the 

 centre of the circumfcribing fphere ; then each of the folid 

 angles made by the four planes meeting at each vertex, will 

 be 4d of the maximum fohd angle ; and each of the folid 

 angles at the bafes of the pyramids will be -rVth of the maxi- 

 mum folid angle. Therefore, each folid angle at the bafe 

 of fuch pyramid is ^th of the fohd angle at its vertex, and 

 if the angle at the vertex be bifefted, either of the folid 

 angles arifing from the bifeftion will be double of either 

 folid angle at the bafe ; hence alfo each folid angle of a 

 prifm with equilateral triangular bafe, will be half each ver- 

 tical angle of thefe pyramids, and double each folid angle 

 at their bafe. 



Solid Figures, Like. See Like. 



Solid Bajlhn. See Bastion. 



Solid Place. See Locus. 



Solid Foot. See Foot. 



Solid Numbers, are thofe which arife from the multipli- 

 cation of a plain number, by any other whatfoever. 



Thus, 18 is a folid number made of 6 (which is plain) 

 multiplied by 3 ; or of 9 multiplied by 2. 



Solid Problem, in MathemaUcs, is one which cannot be 

 geometrically folved, but by the interfeAion of a circle and 

 a conic feftion ; or by the interfeftion of two other conic 

 feftions belides the circle. 



Thus, to defcribe an ifofceles triangle on a given right 

 line, whofe angle at the bafe ihall be triple to that at the 

 vertex, is a folid problem, refolved by the interfedtion of a 

 parabola and a circle. 



Solid Root, among Botanijls, exprefl'es the whole root 

 to be one uniform lump of matter. 



Solid Square, in Military Language, a body of foot 

 where both ranks and files are equal. 



Solid Theorem. See Theorem. 



Solid Celery, in Gardening, that fort which is of a firm 

 crifp nature, without any kind of opening or hoUownefs 

 in the middle part of the Hems. There is a fort of this 

 kind, which has a very flight reddifh tinge, that is greatly 

 cfteemed in fome places. Solid celery commonly eats in a 

 more crifp and agreeable manner than the hollow fort, and 

 on that account is, for the moll part, cultivated in the gar- 

 dens of thoffi who do not raife the plant for fale ; but in 

 the market-gardens, where fale is the great objeft, the com- 

 mon hollow kind is the fort that is the moil in cultivation, 

 as it grows much more quickly, and of courfe becomes 

 fooner ready to be difpofed of in the market, nor does the 

 folid fort Hand the frolt fo well in the winter. Celery be- 

 ing ready at an early penod is a matter of very great im- 

 portance and confideration in thefe fituations, in coniequence 

 of the difference in price being often fo great, as that which 

 is early will not unfrequently fetch double the price, and 

 more, of that which is late. See Apium. 



Neither this folid fort, nor the tall or giant celery, as it is 

 called, are commonly thought fo fit for winter crops. This 

 folid kind was not known until long after the hollow fort 

 had been in ufe, and the above variety is but lately known 

 and cultivated. 



SOLIDAGO, in Botany, from folido, to make firm, 

 and, particularly, to heal a wound ; an old name, fynoni- 

 mous with the Englidi word Confound, and intended to ex- 

 prefs the reputed vulnerary powers of the plants which 

 bore it. — Linn. Gen. 425. Schreb. 556. Willd. Sp. PI. 

 V. 3. 2053. Mart. Mill. Dift. v. 4. Ait. Hort. Kew. 

 V. 5. 64. Sm. Fl. Brit. 889. Prodr. Fl. Grasc. Sibth. 

 V. 2. 179. Purfh 535. Jufl. 181. Lamarck Illullr. 

 t. 680. Gsertn. t. 170. (Virga aurea ; Tourn. t. 275.) 

 Clafs and order, Syngenejia P olygamia-fuperfiua. Nat. Ord. 

 Compofita difcoidex, Linn. Corymbifera, Jufl. 



Gen. Ch. Common Calyx oblong, imbricated, with ob- 

 long, narrow, pointed, ftraight, converging fcales. Cor. 

 compound, radiated. Florets of the diflc numerous, per- 

 feft, tubular, funnel-fhaped, with a five-cleft fpreading 

 limb ; thofe of the radius fewer than ten, ufually five, 

 ligulate, lanceolate, three-toothed, female. Stam. in the 

 perfeft florets. Filaments five, capillary, very ftiort ; an- 

 thers united into a cylindrical tube. Pifi. in the fame 

 florets, Germen oblong ; ftyle thread-fliaped, the length of 

 the fl;amens ; ftigma cloven, fpreading : in the female orves, 

 Germen and fl;yle as in the former ; Itigmas two, revolute. 

 Perle. none, the calyx remaining fcarcely changed. Seeds 

 iolitary to each floret of the dilk, obovate-oblong. Down 

 4 capillary. 



